2 schools of thought, here, and I've tried both on a 99 and 2000 with the same issue. Here's what I can offer: The issue with 1ZZ's of this era is that the oil return holes in the pistons aren't sufficient and eventually clog up; in most cases, it has nothing to do with the rings until (and unless) it's been let go for too long.
Knowing this crucial piece of information, you can deduce that the most important first step is to restore oil flow. Since we're talking about (hopefully only partially) clogged passageways (the oil return holes), that means thinner, not thicker, oil. I had luck with Pennzoil Platinum 0w20 in the 99 (completely stopped consumption in 2 OCIs, no consumption when I sold it a year later) and Pennzoil Ultra 5w20 in the 2000 (they don't make a 0w20 Ultra or I'd have used it).
In the 2000, I greatly reduced the consumption, but didn't stop it. In this case, I was able to clear out the oil return holes but I either have stuck or cracked rings (this hypothesis is backed by compression numbers; and I'm leaning toward stuck since the numbers weren't that
bad). I'm currently running Rotella T6 (which is a 5w40 HDEO) to try and clean that up; I'm also performing another experiment using canola oil, so any further results I could report on that front won't be valid in your case (e.g. ignore most of this paragraph, it's really just informational and not at all suggesting you follow this path).
Basically, assuming your oil return holes aren't completely clogged, the most likely case is you need to run something thinner for a while (1-2 OCI) to begin clearing out the clogged oil return holes before any additive, cleaner, or heavy duty oil will even be able to touch the issue. If that slows, but doesn't completely stop the consumption, then
you should use a cleaning additive to attempt to free possibly-stuck rings.
And, of course, once you've managed to stop the consumption, consider switching back to the recommended 5w30. Oh, and don't be gentle with it just because it's sick; it's important to get it moving, or you'll only be contributing to the problem.